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A024785
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Left-truncatable primes: every suffix is prime and no digits are zero.
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26
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2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197, 223, 283, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 523, 547, 613, 617, 643, 647, 653, 673, 683, 743, 773, 797, 823, 853, 883, 937, 947, 953, 967, 983, 997, 1223
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OFFSET
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1,1
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COMMENTS
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Last term is a(4260) = 357686312646216567629137 (Angell and Godwin). - Eric Weisstein, Dec 11 1999
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..4260 (The full list, based on the De Geest web site)
Index entries for sequences related to truncatable primes
I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.
P. De Geest, The list of 4260 left-truncatable primes
Rosetta Code, Programs for finding truncatable primes
Eric Weisstein's World of Mathematics, Truncatable Prime
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MAPLE
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a:=[[2], [3], [5], [7]]: l1:=1: l2:=4: for n from 1 to 3 do for k from 1 to 9 do for j from l1 to l2 do d:=[op(a[j]), k]: if(isprime(op(convert(d, base, 10, 10^nops(d)))))then a:=[op(a), d]: fi: od: od: l1:=l2+1: l2:=nops(a): if(l1>l2)then break: fi: od: seq(op(convert(a[j], base, 10, 10^nops(a[j]))), j=1..nops(a)); # Nathaniel Johnston, Jun 21 2011
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MATHEMATICA
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max = 2000; truncate[p_] := If[id = IntegerDigits[p]; FreeQ[id, 0] && (Last[id] == 3 || Last[id] == 7) && PrimeQ[q = FromDigits[ Rest[id]]], q, p]; ok[n_] := FixedPoint[ truncate, n] < 10; p = 5; A024785 = {2, 3, 5}; While[(p = NextPrime[p]) < max, If[ok[p], AppendTo[A024785, p]]]; A024785 (* From Jean-François Alcover, Nov 09 2011 *)
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PROG
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(PARI) {v=vector(4260); v[1]=2; v[2]=3; v[3]=5; v[4]=7; i=0; j=4; until(i>=j, i++; p=v[i]; P10=10^(1+log(p)\log(10)); for(k=1, 9, z=k*P10+p; if(isprime(z), j++; v[j]=z; ))); s=vector(4260); s=vecsort(v); for(i=1, j, write("b024785.txt", i, " ", s[i]); ); } [From Harry J. Smith, Sep 19 2008]
(Haskell)
import Data.List (tails)
a024785 n = a024785_list !! (n-1)
a024785_list = filter (\x ->
all (== 1) $ map (a010051 . read) $ init $ tails $ show x) a038618_list
-- Reinhard Zumkeller, Nov 01 2011
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CROSSREFS
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Cf. A033664, A032437, A020994, A024770 (right-truncatable primes), A052023, A052024, A052025, A050986, A050987, A077390 (left-and-right truncatable primes), A137812 (left-or-right truncatable primes)
Sequence in context: A067905 A042993 A033664 * A069866 A125772 A001000
Adjacent sequences: A024782 A024783 A024784 * A024786 A024787 A024788
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KEYWORD
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nonn,base,easy,fini,full
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AUTHOR
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David W. Wilson
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STATUS
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approved
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